Related papers: Testing with p*-values: Between p-values, mid p-va…
We consider the problem of comparing two Poisson parameters from the Bayesian perspective. Kawasaki and Miyaoka (2012b) proposed the Bayesian index $P(\lambda_1 < \lambda_2 | X_1,X_2)$ and expressed it using the hypergeometric series. In…
Permutation $p$-values have been widely used to assess the significance of linkage or association in genetic studies. However, the application in large-scale studies is hindered by a heavy computational burden. We propose a geometric…
In the field of multiple hypothesis testing, combining p-values represents a fundamental statistical method. The Cauchy combination test (CCT) (Liu and Xie, 2020) excels among numerous methods for combining p-values with powerful and…
In this paper we develop with considerable details a theory of multivector functions of a $p$-vector variable. The concepts of limit, continuity and differentiability are rigorously studied. Several important types of derivatives for these…
The established language for statistical testing --- significance levels, power, and p-values --- is overly complicated and deceptively conclusive. Even teachers of statistics and scientists who use statistics misinterpret the results of…
Often in sequential trials additional data become available after a stopping boundary has been reached. A method of incorporating such information from overrunning is developed, based on the ``adding weighted Zs'' method of combining…
It is common for genomic data analysis to use $p$-values from a large number of permutation tests. The multiplicity of tests may require very tiny $p$-values in order to reject any null hypotheses and the common practice of using randomly…
This paper considers the problem of testing many moment inequalities where the number of moment inequalities, denoted by $p$, is possibly much larger than the sample size $n$. There is a variety of economic applications where solving this…
The pairwise winning indices, computed in the Stochastic Multicriteria Acceptability Analysis, give the probability with which an alternative is preferred to another taking into account all the instances of the assumed preference model…
The cell biology literature is littered with erroneously tiny P values, often the result of evaluating individual cells as independent samples. Because readers use P values and error bars to infer whether a reported difference would likely…
Our interest is whether two binomial parameters differ, which parameter is larger, and by how much. This apparently simple problem was addressed by Fisher in the 1930's, and has been the subject of many review papers since then. Yet there…
In this article, we consider the problem of constructing the confidence interval and testing hypothesis for the common coefficient of variation (CV) of several normal populations. A new method is suggested using the concepts of generalized…
Equivalence tests, otherwise known as parity or similarity tests, are frequently used in ``bioequivalence studies" to establish practical equivalence rather than the usual statistical significant difference. In this article, we propose an…
We introduce the E-measure: a measure-like generalization of the E-value to a class of hypotheses. Unlike classical measures, E-measures are closed under infimums instead of addition. They arise from a compatibility axiom with logical…
Distance correlation is a measure of dependence between two paired random vectors or matrices of arbitrary, not necessarily equal, dimensions. Unlike Pearson correlation, the population distance correlation coefficient is zero if and only…
Probabilistic classifiers output a probability distribution on target classes rather than just a class prediction. Besides providing a clear separation of prediction and decision making, the main advantage of probabilistic models is their…
We develop the theory of hypothesis testing based on the e-value, a notion of evidence that, unlike the p-value, allows for effortlessly combining results from several studies in the common scenario where the decision to perform a new study…
We discuss $p$-variation regularity of real-valued functions defined on $[0,T]^2$, based on rectangular increments. When $p>1$, there are two slightly different notions of $p$-variation; both of which are useful in the context of Gaussian…
A common problem in genetics is that of testing whether a set of highly dependent gene expressions differ between two populations, typically in a high-dimensional setting where the data dimension is larger than the sample size. Most…
Multi-class classification methods that produce sets of probabilistic classifiers, such as ensemble learning methods, are able to model aleatoric and epistemic uncertainty. Aleatoric uncertainty is then typically quantified via the Bayes…